I have simulated the behavior of two variables over the course of three weeks:
var_1 <- ts(c(25.1,21.8,15.6,28.0,25.8,26.2,29.9,30.6,28.3,22.1,20.2,20.5,18.4,12.0,8.1,8.6,8.2,9.17,8.8,9.7,10.4)) var_2<-ts(c(-13.1,-7.5,0.1,-3.4,-6.0,-4.6,-0.1,4.8,4.3,-1.1,-6.5,-10.0,-9.2,-7.8,-7.6,-7.1,-11.4,-14.2,-19.6,-22.9,-23.5))
var_1 is the independent variable and I would like to see if var_2 is influenced by its fluctuations.
In the figure above (A), var_1 is in black and var_2 in red. Just looking at the curves, I would say that a relationship exists at least until around day 12, then some major lag occurs.
My first idea to highlight any similarity was to apply a running correlation test (fig. B above). I used the function
running() from the R library
running(var_1, var_2, fun=cor, width=5)
The overlapping window has a width of 5 days. The 95% significance boundaries (dashed red lines) are calculated by running 999 simulations of randomly generated data sets with the same structure.
The correlation is rather good between day 6 and 12, but it is never statistically significant. Is there a more appropriate way to point out any common behavior?
Additionally, I tried to apply a cross correlation function to check for significant lags (R function
It shows a strong correlation for lags -3 to 0 with tapering in both directions. If I interpret it correctly, I suppose I could say that it takes 0 to 3 days for var_2 to react to any change in var_1.
While this result is extremely interesting, I feel it does not describe well all the dynamics between the two curves, such as the good correlation limited to day 6 and 12. But, as seen above, the test that could do it does not show any statistical significance. So I am a bit puzzled as to what can be the most fitting method to describe these data.